﻿60 Dr. Gr. Green on Fluid Motion 



The motions considered above are motions of any incom- 

 pressible fluid and do not indicate, except as approximations, 

 conditions of motion possible in the atmosphere, One or 

 two solutions of a similar type can be obtained which refer 

 to incompressible fluid and accordingly represent motions 

 possible in the atmosphere. Consider now the motion repre- 

 sented by 



«=-©(y-^); 5 v=0; m? = 0. . . (29) 



The equations of motion of any element of fluid in this 

 case are 



°=- 9 i- k h logp ' ■ (30) 



-20 sin </> . oo(y-!3z) = ~ || -k^-logp, . (31) 



2OooB*«(y-^)=-^-^lo g/0 , . (32) 



and these equations are satisfied provided the pressure 

 system throughout the fluid is that indicated by 



ilogp = n«a*. a>(y-/3zy- 9 (^f + «) + Mogp , (33) 



where /3 = cot.$, and p is the density of the fluid at the 

 reference point O. The continuity equation is also satisfied 

 provided we can neglect the term (go)/R),v(y — ftz). This 

 condition limits considerably the extent of the region 

 around to which our solution is applicable, as stated 

 earlier. Within the region to which the above applies the 

 isobars at the surface of the Earth run East and West, 

 being determined by 



h log p = 12 sin </> . coy 2 -f k log p Q , . * . (34) 



which indicates a system symmetrical on the two sides of 

 the East and West line drawn through reference point 0. 

 In this case the isobars become closer as we proceed North 

 or South from point 0. They are also parallel to the lines 

 of flow of the fluid. 



The coefficient ^ has the value 1*5 x 10~ 6 with the foot 



and the second as units; while 2D sin (j> has the value 

 1*03 x 10 ~ 4 at latitude 45°. Certain cases of interest arise 



in which the terms containing ~ may be neglected. For 



